Solving Equations and Word Problems

This lesson covers various mathematical concepts related to balance and equations. Students learn to select and write equations representing hangers, reason with equations to find unknown values, and match equations to diagrams. The lesson also includes practical applications like calculating side lengths of rectangles and understanding savings as percentages of a goal.

Which of the following equations correctly represents the hanger with three x's balancing with six ones?

• x + x + x = 1 + 1 + 1 + 1 + 1 + 1

• x + x = 1 + 1 + 1 + 1

• 3x = 5

• x = 6

What equation represents a hanger with two x's and three balancing with a total of five?

• 2x = 5

• x + 3 = 5

• x = 5

• 2x + 3 = 5

How would you find the value of x in the equation 2x = 14.62?

• Multiply both sides by 2

• Divide both sides by 2

• Subtract 2 from both sides

• Add 2 to both sides

Why is Andre's reasoning incorrect when he claims x is seven?

• He added instead of subtracting

• He used the wrong equation

• He moved terms incorrectly, disrupting balance

• He correctly balanced the equation

Which diagram matches the equation 12 - m = 4?

• Diagram A

• Diagram B

• Diagram C

• Diagram D

If the area of a rectangle is 14 and one side is 2 1/3, what is the length of the other side?

• 5

• 4

• 3

• 6

What is the unknown side length if the area is 14 and one side is 4 1/5?

• 5

• 4

• 2 1/3

• 3 1/3

How much has Lynn saved if she has reached 25% of her $20 goal?

• $10

• $5

• $20

• $15

If Lynn has saved 75% of her goal, how much money does she have?

• $25

• $20

• $15

• $10

What is the total amount saved if Lynn has reached 125% of her $20 goal?

• $30

• $25

• $20

• $15